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Hypothesis Testing with R
P-Values

You know that a hypothesis test is used to determine the validity of a null hypothesis. Once again, the null hypothesis states that there is no actual difference between the two populations of data. But what result does a hypothesis test actually return, and how can you interpret it?

A hypothesis test returns a few numeric measures, most of which are out of the scope of this introductory lesson. Here we will focus on one: p-values. P-values help determine how confident you can be in validating the null hypothesis. In this context, a p-value is the probability that, assuming the null hypothesis is true, you would see at least such a difference in the sample means of your data.

Consider the experiment on history and chemistry majors and their interest in volleball from a previous exercise:

  • Null Hypothesis: "History and chemistry students are interested in volleyball at the same rates"
  • Experiment Sample Means: 34% of history majors and 39% of chemistry majors sign up for the volleyball class

A hypothesis test on the experiment data that returns a p-value of 0.04 would indicate that, assuming the null hypothesis is true and there is no difference in preference for volleyball between all history and chemistry majors, you would see at least such a difference in sample mean (39% - 34% = 5%) only 4% of the time due to sampling error.

Essentially, if you ran this same experiment 100 times, you would expect to see as large a difference in the sample means only 4 times given the assumption that there is no actual difference between the populations (i.e. they have the same mean).

Seems like a really small probability, right? Are you thinking about rejecting the null hypothesis you originally stated?

Instructions

1.

You are big fan of apples, so you gather 10 green and 10 red apples to compare their weights. The green apples average 150 grams in weight, and the red apples average 160 grams in weight.

You run a hypothesis test to see if there is a significant difference in the weight of green and red apples. The test returns a p-value of 0.2. Which statement (st_1, st_2, st_3, or st_4) indicates how this p-value can be interpreted?

Update the value of interpretation with the string "st_1", "st_2", "st_3", or "st_4" depending on your answer.

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